The rectangulus was an astronomical instrument made by

Richard of Wallingford Richard of Wallingford (1292–1336) was an English mathematician, astronomer, horologist, and cleric who made major contributions to astronomy and horology while serving as abbot of St Albans Abbey in Hertfordshire. Biography Richard was b ...

around 1326. Dissatisfied with the limitations of existing

astrolabe An astrolabe (; ; ) is an astronomy, astronomical list of astronomical instruments, instrument dating to ancient times. It serves as a star chart and Model#Physical model, physical model of the visible celestial sphere, half-dome of the sky. It ...

s, Richard developed the rectangulus as an instrument for

spherical trigonometry Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the edge (geometry), sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, ge ...

and to measure the angles between planets and other astronomical bodies. This was one of a number of instruments he created, including the ''

Albion Albion is an alternative name for Great Britain. The oldest attestation of the toponym comes from the Greek language. It is sometimes used poetically and generally to refer to the island, but is less common than "Britain" today. The name for Scot ...

'', a form of

equatorium An equatorium (plural, equatoria) is an astronomy, astronomical Mechanical calculator, calculating instrument. It can be used for finding the positions of the Moon, Sun, and planets without arithmetic operations, using a geometrical model to re ...

, and a famously complicated and expensive horologium (

astronomical clock An astronomical clock, horologium, or orloj is a clock with special mechanisms and dials to display astronomical information, such as the relative positions of the Sun, Moon, zodiacal constellations, and sometimes major planets. Definition ...

). His ''Tractus Rectanguli'', describing the rectangulus, was an influential text in medieval astronomy and at least thirty copies were known to survive. His ''Quadripartitum'' was the first text on spherical trigonometry to be published in Western Europe. The rectangulus was a form of skeleton torquetum. This was a series of nested angular scales, so that measurements in azimuth and elevation could be made directly in polar coordinates, relative to the

ecliptic The ecliptic or ecliptic plane is the orbital plane of Earth's orbit, Earth around the Sun. It was a central concept in a number of ancient sciences, providing the framework for key measurements in astronomy, astrology and calendar-making. Fr ...

. Conversion from these coordinates though was difficult, involving what was the leading mathematics of the day. The rectangulus was an analogue computing device to simplify this: instead of measuring in angular measurements it could resolve the angles to Cartesian components directly. This then simplified the further calculations. The rectangulus was constructed as a brass pillar with a number of linear scales hinged above it. Pinhole sights on the upper arm allowed it to be pointed accurately at the astronomical target.

Plumb bob A plumb bob, plumb bob level, or plummet, is a weight, usually with a pointed tip on the bottom, suspended from a string and used as a vertical direction as a reference line, or plumb-line. It is a precursor to the spirit level and used to esta ...

lines descended from the scales above and intersected with linear scales marked on the horizontal scales below. These allowed measures to be read, not as angles, but as trigonometric ratios. To celebrate the 600th anniversary of the Rectangulus in 1926 a replica was constructed. This is now in the History of Science Museum, Oxford.

References

{{Reflist, colwidth=35em, refs= {{Cite web , title=Model of the "Rectangulus" of Richard of Wallingford , id=10928 , publisher= Museum of the History of Science , url=http://www.mhs.ox.ac.uk/collections/imu-search-page/record-details/?TitInventoryNo=10928&querytype=field&thumbnails=&irn=17054 {{Cite book , title=Cosmos: An Illustrated History of Astronomy and Cosmology , first=John , last=North , publisher=

University of Chicago Press The University of Chicago Press is the university press of the University of Chicago, a Private university, private research university in Chicago, Illinois. It is the largest and one of the oldest university presses in the United States. It pu ...

, year=2008 , isbn=978-0226594415 , pages=259–261 {{Cite book , title=God's Clockmaker , first=John , last=North , year=2007 , publisher=A&C Black , isbn=978-1852855710 , url=https://books.google.com/books?id=XIytAwAAQBAJ&pg=PA349 , pages=348–350 {{Cite book , title=The Medieval Machine , first=Jean , last=Gimpel , authorlink=Jean Gimpel , year=1992 , origyear=1976 , edition=2nd , publisher=Pimlico , isbn=978-0-7126-5484-5 , pages=155–157 {{Cite web , title=Richard of Wallingford: Abbot of St. Albans, 1326-1335 , publisher=St. Albans and Herts Architectural and Archaeological Society. , url=https://www.stalbanshistory.org/wp-content/uploads/2019/05/1926_05_.pdf , pages=236–237, 239 {{Cite journal , title=Richard of Wallingford and his Rectangulus , first=R.T. , last=Gunther , journal=

Nature Nature is an inherent character or constitution, particularly of the Ecosphere (planetary), ecosphere or the universe as a whole. In this general sense nature refers to the Scientific law, laws, elements and phenomenon, phenomena of the physic ...

, volume=118 , issue=2978 , pages=773–774 , date=27 November 1926 , doi=10.1038/118773a0 , bibcode = 1926Natur.118..773G , doi-access=free {{Cite journal , last=Michel , first=H. , title=Le Rectangulus de Wallingford , year=1944 , journal=Ciel et Terre , volume=60 , pages=11–12 , bibcode=1944C&T....60..196M Astronomical instruments Historical scientific instruments Mechanical calculators